The invention relates to educational and amusement devices utilizing one or more boards having one or more rectangular playing fields or areas and one or more sets of 18 different one-sided pentominoes.
Pentominoes are a species of polyominoes which are shapes made by connecting equal-sized squares of various numbers so that each square has a full edge connection with at least one other square. The polyomino sequence begins with the lowest polyomino, the domino which has two squares and progresses to the tromino having three squares, the tetromino having four squares, the pentomino having five squares, the hexomino having six squares, the heptomino having seven squares, etc.
The branch of mathematics dealing with ways in which these geometric shapes may be arranged or combined is called combinatorial geometry. It is a very useful and complex field of mathematics which, however, does not lend itself yet to treatment by formulas and equations. For example, no equation is known for determining the number of the various ominoes. Moreover, since each piece is capable of rotation, i.e., angular motion around an axis perpendicular to the bottom surface of the piece on a supporting surface, and reflection, i.e., flipping the piece over so that its bottom surface becomes its top surface, the combining possibilities rapidly increase as the number of ominoes increases. Some polyominoes have reflective symmetry, i.e., the same configuration on reflection, while others do not. If polyominoes are excluded which have reflective symmetry, i.e., both broad surfaces of each polyomino are, or are considered, the same in appearance they are known as two-sided polyominoes and the number of two-sided ominoes for each numbers of squares from dominoes to heptominoes is as follows: NUMBER OF SQUARES NUMBER OF TWO-SIDED OMINOES ______________________________________ dominoes (2) 1 trominoes (3) 2 tetrominoes (4) 5 pentominoes (5) 12 hexominoes (6) 35 heptominoes (7) 108 ______________________________________
If polyominoes that have relfective symmetry and their reflective symmetrical counterparts are included, i.e., the two broad surfaces of each polyomino are different in appearance they are known as one-sided polyominoes and the number thereof is larger than the number of two-sided polyominoes. With tetrominoes and pentominoes, for example, if reflection is eliminated, the number of ominoes increases from five two-sided, to seven one-sided tetrominoes and from 12 two-sided to 18 one-sided pentominoes.
The educational and amusement device of the present invention contemplates not only the various combinations of the boards and the pieces but also a novel board and novel sets of pentominoes.
Polyomino games and puzzles have been proposed in prior literature and patents. Reference in this connection is made to a book entitled "POLYOMINOES" by Solomon W. Golomb, Charles Scribner in New York, N. Y., 1965 and the bibliography therein, and to U.S. Pat. No. 2,900,190 granted to Jules Pestieau on Aug. 18, 1959. The prior art, however, does not disclose the present invention or make it obvious to one of ordinary skill in this art.